In lamenting President Barack Obama's foreign and military policies, Republicans have frequently offered a concise summary: "Our allies don't trust us, and our enemies don't fear us." They didn't imagine the day would come when the same might be said of a Republican president. But that's the prospect Donald Trump raises.

The latest source of alarm is an interview the president-elect gave to The Times of London and the German newspaper Bild. First he reiterated his unflattering view of the Atlantic alliance. "I took such heat when I said NATO was obsolete," he said. "And then they started saying, 'Trump is right.' " As for the country that poses the main military threat to Europe, he said, "Let's see if we can make some good deals with Russia."

He dismissed the European Union: "Personally, I don't think it matters much for the United States. ... I don't really care if it's separate or together." He said the British vote to leave the EU was "a great thing." He added vague caveats: "NATO is very important to me," and "I feel very strongly toward Europe."

These remarks didn't go beyond what he said during his presidential bid, when he frequently accused our NATO allies of not paying their fair share, while insisting, "If we can make a great deal for our country and get along with Russia, that would be a tremendous thing." He also said he expected the EU to "break up" over the problem of refugees. But words uttered by an incoming president carry far more weight. His latest pronouncements "caused astonishment and excitement, not just in Brussels," said Germany Foreign Minister Frank-Walter Steinmeier, who noted that they contradicted the positions taken by his nominee for defense secretary, James Mattis, in his confirmation hearings.

NATO, of course, has been the most successful military alliance ever seen, keeping the peace among nations that, before its creation in 1949, were repeatedly drenched in gore. It also has served as a sturdy check on Russian expansionism, while providing a way for Germany to work amicably and productively with countries that once were its enemies. The 28-member EU has advanced parallel purposes by removing trade barriers, establishing a common currency and allowing free travel.

Neither has been without fault. Most NATO countries have fallen short of the commitments they have made on military spending. The EU has often promoted tone-deaf overregulation from its Brussels headquarters, and the flood of refugees in recent years has made its open borders problematic.

But NATO also sent troops to Afghanistan to help the United States after 9/11. The EU has helped dampen the worst elements of nationalism.

If Trump is merely making a calculated attempt to force laggard governments to meet their obligations, more power to him. Brexit and his disparagement of the EU could encourage refugee policies that satisfy popular anxieties. Maybe Trump can devise ways to work with Russia on matters of common concern without reneging on our security commitments.

But no one in Europe should ever be induced to wonder if America is on the side of Europe's free and democratic nations or the menacing, corrupt autocrat in the Kremlin. The military partnerships and economic connections between the United States and Europe deserve a great deal of the credit for the relative peace and prosperity of the postwar era.

Efforts to improve this system of cooperation should always be welcomed. But they should also be careful. As with most structures, renovation is wiser than demolition.